Currently, the native Sugar CRM mobile app does not support offline mode for any sugar version but there is another app named RSugar that supports offline, online and cache mode but for Sugar versions less than 7. RSugar version that supports Sugar 7 in both offline and online mode is being developed and it will be out shortly in Apple and Google stores. To check out this app, follow the links:

It actually does support a mode called offline Cache, which caches all records read, favorited, or owned by user, or first 100 of each module, up to storage limit of mobile IOS or android device. So if you wanted it all, use ETL or excel plugin to set the favorite flag for whole module (every field), sync your mobile then turn off the favorites same way (keep a list of what you really wanted favorited :) )